3 Answers
3

there is a good information about these terms on Basudeb Bhatta's Blog at this link.
@Brad Nesom definations are good but i thought that geodata was abbrevation of geographic data. However Brad's defination of geodata is quite logical.

beside these in my opinion:

spatial data > geospatial data == geographic data == geodata

...

Often my students ask about the difference(s) between spatial and
geospatial. These two words appear very frequently in remote sensing
and GIS literature.

The word spatial originated from Latin 'spatium', which means space.
Spatial means 'pertaining to space' or 'having to do with space,
relating to space and the position, size, shape, etc.' (Oxford
Dictionary), which refers to features or phenomena distributed in
three-dimensional space (any space, not only the Earth's surface) and,
thus, having physical, measurable dimensions. In GIS, 'spatial' is
also referred to as 'based on location on map'.

Geographic(al) means 'pertaining to geography (the study of the
surface of the earth)' and 'referring to or characteristic of a
certain locality, especially in reference to its location in relation
to other places' (Macquarie Dictionary). Spatial has broader meaning,
encompassing the term geographic. Geographic data can be defined as a
class of spatial data in which the frame is the surface and/or
near-surface of the Earth. 'Geographic' is the right word for graphic
presentation (e.g., maps) of features and phenomena on or near the
Earth's surface. Geographic data uses different feature types (raster,
points, lines, or polygons) to uniquely identify the location and/or
the geographical boundaries of spatial (location based) entities that
exist on the earth surface. Geographic data are a significant subset
of spatial data, although the terms geographic, spatial, and
geospatial are often used interchangeably.

Geospatial is another word, and might have originated in the industry
to make the things differentiate from geography. Though this word is
becoming popular, it has not been defined in any of the standard
dictionary yet. Since 'geo' is from Greek 'gaya' meaning Earth,
geospatial thus means earth-space. NASA says 'geospatial means the
distribution of something in a geographic sense; it refers to entities
that can be located by some co-ordinate system'. Geospatial data is to
develop information about features, objects, and classes on Earth's
surface and/or near Earth's surface. Geospatial is that type of
spatial data which is related to the Earth, but the terms spatial and
geospatial are often used interchangeably. United States Geological
Survey (USGS) says "the terms spatial and geospatial are equivalent".

Sometimes I might ask if the data has either temporal or location information, and then get into details about how to use it. Really this is no different than asking if a column in the database is float, decimal, or money. Significantly different to work with -- you need to know your data.

So I do not define the data as spatial or not, I simply expect to see either geography or geometry columns (or create them if need be).

Usually the collection, view, or USE CASE of the data becomes the defining term we will use, e.g. "These data are for prioritizing the underground tank clean up based on the volume and depth of the leaking hazard" or "This maps the water pressure deliverable across the city at fire hydrants."

In sum: we don't call it financial data, or monetary data, or spatial data. Its just data, sometimes with a geometry or geography column.

Since this is a Community WIKI this is my opinion.
As for actual definitions I don't know. And how (or why J) you write a scientifc paper as well.
But what I see in my mind is this.
geospatial data, spatial data can be data in any format with any coordinate reference in any storage type.
geographic data (outside the national geographic context) is rdbms native spatially enabled lat/lon data.
geodata is any type of data as a service served by a web server.
Again I re-iterate that these are NOT definitions simply how I use the terms in context when discussing and how I think of them to keep stuff seperate. FWIW.